I will give this a brief shot. There are two basic but different ways to look at modes. They each have their own purpose and use. I am going to use D Dorian as an example and look at it two different ways:
1. A Dorian mode is like a natural minor scale, but the 6th is raised a half step. Compare a D minor natural minor scale, and a D Dorian scale:
D, E, F, G, A, B-flat, C, D
D, E, F, G, A, B, C, D
This is a good example to compare the similarities and differences between a mode and its minor or major counterpart. As listeners, we can hear that raised 6th and the unique flavor it provides. The unexpected major IV chord (G) also helps to emphasize this as well as the unexpected minor ii chord. Looking at the mode in this way really helps to understand how it is unique. While it is similar to minor, it offers its own attributes. This particular way of looking at any of the modes can be helpful in understanding it, but it does absolutely nothing to understand how it relates to the key. For that, take a look at it from another perspective:
2. Here it is again:
D, E, F, G, A, B, C, D
Now, think about the key signature. No sharps or flats. We understand that C major and A minor are relatives. D Dorian is also a relative. I am not a composer. I am a teacher and a secondary performer. This second way of looking at modes is what speaks to me, and what I share with my students.
Over half of my students cross train. As soon as a student learns their first major scale form, I introduce my cross trainers to basic improvisation using the major scale form. They are always happily surprised at the many flavors of music they are producing just by playing in a scale form. While perhaps not relevant to what YOU are seeking, this is more of what I meant in my earlier post about players really needing to see the shapes of the scale forms on the fret board.
In the name of practicality, understanding that a Dorian mode is a minor scale with a raised 6th does nothing to help me readily use the scale. Of course I UNDERSTAND it, but it doesn't help me learn to master my Dorian scales. Knowing the relative major scale, and knowing my major scale forms on the guitar does.
While I've used the Dorian mode as an example, this applies to all of the modes. And this also applies to all of the Jazz modes derived from the relative melodic minor scales. As players, yes it is important to understand the unique attributes of the various modes, but it doesn't help us play them. Seeing how they relate to relative keys and knowing our scale forms helps us play them.
Dr. Todd Tipton, Noda Guitar Studio
Charlotte, NC, USA (available via Skype)